Introduction
This activity illustrates the principle of univariance in color perception. A graph is shown with wavelength on the x-axis and maximum response rate on the y-axis. The response curve plotted is shaped like an inverted U and starts at 400, is highest at 550, and drops back to 0 at 675. Two “lights” are shown below the graph: Light #1 is light blue with an amplitude of 90% and Light #2 is dark blue with an amplitude of 10%. Light #2 can be changed, and the user can pick between five colors of wavelengths 450, 500, 550, 600, and 650 corresponding to dark blue, light blue, green, yellow, and red, respectively. For each color, the user can choose one of five amplitudes (90% bright to 10% bright in steps of 20%). Beneath both lights is a box showing an oscilloscope output of how often a neuron is spiking per second in response to each light. Most of colors that Light #2 can be set to produce a different pattern of neural spiking than Light #1. However, when Light #2 is set to wavelength 500 at 90% amplitude, wavelength 550 at 70% amplitude, or wavelength 600 at 90% amplitude, it produces a spike pattern as Light #1.
The most important thing to notice in this activity is that it is possible to create the same firing rate for both lights with several different wavelength and amplitude combinations—this is the principle of univariance.
The Principle of Univariance
In a nutshell, the principle of univariance states that an infinite set of different wavelength-intensity combinations can elicit the same response from a single type of photoreceptor. This creates a problem for perception which is that we want to be able to perceive two aspects of light—wavelength and amplitude—corresponding to color and brightness. However, a single type of cone can only provide one piece of information—a neural firing rate. In other words, the firing rate of the receptor cell varies in only one dimension (it is “univariate”), but we need to code for two dimensions of the stimulus. This problem is so serious that if we had only one type of cone, we would not have color vision at all!
The graph at the top left plots the maximum firing rate of one type of cone receptor for lights ranging from 400 to 700 nanometers (nm). Remember that retinal receptor cells respond with faster firing rates the more intense a light is. That is, bright lights tend to elicit faster firing rates than dim lights. However, as the graph illustrates, a cone’s firing rate is also determined by the wavelength of the light. This cone type “prefers” lights of about 550 nm (green). This means that if we have two lights of equal amplitude, the one closer to 550 nm (green) will elicit a greater response from the cone.
If the input to Light #2 is changed, the cone’s firing rate changes depending on which light is selected. Bright lights closest to 550 nm (green) yield the highest firing rates. Dim lights farthest from 550 nm (green) yield the lowest firing rates. Once you understand how the selection of Light #2 is reflected in the cone’s response rate, move on to the next section.
Demonstrating the Principle
Below the graph, we see a simulation of the cone’s firing rate to two lights. Light #1 is fixed at a wavelength of 500 nm (light blue) and an amplitude of 90% (where 0% and 100% simulate very dark and very bright lights, respectively). As shown in the rectangle just below the graph, this light will be perceived by most humans as a bright, sky-blue color. But the only thing this single cone tells us is that the light stimulates the cone causing a retinal ganglion cell to fire action potentials at the rate illustrated in the black rectangle. This rectangle mimics the output of an oscilloscope recording the activity of a retinal ganglion cell that takes input from a single cone. Each green line represents an action potential, so the more green lines you see per second, the faster the firing rate.
When the page first loads, Light #2 is set to 450 nm and 10% amplitude perceived as a very dark blue by most humans. This light does not elicit much of a response from this type of cone. However, the user can change the wavelength and amplitude of the light by clicking in the colored squares below it. Some experimentation by the user reveals that the same neural firing pattern can be produced with colors other than sky blue.
Questions
If you think you understand this activity (or even if you do not yet fully understand), try answering the following questions. Note that question 5 is crucial for understanding the principle of univariance.
Q1. Which light produces the fastest response rate?
The 550-nm (green) light at 90% amplitude causes the cone to fire most rapidly. This is predictable from the graph: the peak of the curve shows that 550-nm (green) lights have the highest maximum response rates for this cone. The 90%-amplitude lights push the cone to a response rate close to the maximum rate shown the graph. If you start with the 450-nm (dark blue), 90% light and move right (clicking next on the 500-nm [sky blue], 90% light, then on the 550-nm [green], 90% light, etc.), you will see the response rate of the cone begin to go up, reach its peak at 550 nm (green), and then begin to go down. The 450-nm (dark blue) and 650-nm (red) lights are farthest from the peak and so produce the smallest neural responses.
Q2. Which lights produce the slowest response rate (a number of lights tie for this honor)?
Any light at 10% amplitude produces the same, very slow, response rate. All neurons fire spontaneously even when they are not being stimulated at all. In our demonstration, none of the very dim (10%) lights are strong enough to push the cone past its spontaneous firing rate. More interestingly, a number of other lights also fail to push the cone past its spontaneous rate even when they are increased past 10% amplitude, as noted in the answers to Questions 3 and 4.
Q3. What happens to the response rate as you move up in amplitude for 600-nm (yellow) lights?
As discussed in the answer to Question 2, the 600-nm (yellow), 10%-amplitude light is not strong enough to push the cone past its baseline (spontaneous) firing rate. In fact, since 600 nm (yellow) is fairly distant from the cone’s peak wavelength of 550 nm (green), increasing the amplitude to 30% still fails to produce a response greater than baseline. However, as the amplitude is increased to 50%, 70%, and 90%, the cone’s response rate finally increases beyond the baseline firing rate.
Q4. What happens to the response rate as you move up in amplitude for 650-nm (red) lights?
Even at 90% of maximum amplitude, the cone does not respond at all (it fires at its baseline rate) to 650-nm (red) lights. Again, this is predictable from the response rate graph: the maximum response rate for this wavelength is essentially 0. This type of cone just does not respond to 650-nm (red) lights (or higher). (Note that if this were the only type of receptor we had, 650-nm (red) light would be invisible to us, just as other forms of electromagnetic radiation outside of this cone’s receptive range, such as ultraviolet and infrared rays, are invisible to humans.)
Q5. Can you find a wavelength–amplitude combination for Light #2 that produces the exact same firing rate as Light #1?
In fact, there are two other lights that produce the same firing rate as 500 nm (sky blue) at 90%: a 550-nm (green) light at 70% amplitude and a 600-nm (yellow) light at 90%. You should realize that if we were able to enter any other values we wished for wavelength and amplitude, there would be even more examples (525 nm [bluish green] at 80% and 560 nm [yellowish green] at 85% are two examples).
This is why we cannot code for both wavelength and amplitude with a single receptor. The maximum firing rate can only be elicited from this cone by a 550-nm (green) light at high amplitude, but a medium-strength firing rate could be caused by a 550-nm (green) light at medium amplitude, a 475-nm (medium blue) light at really high amplitude, a 590-nm (greenish yellow) light at an in-between amplitude, and so on.
So how do we overcome the principle of univariance to achieve color vision? The answer is that we use the pattern of responses across multiple types of cones to determine both the wavelength and amplitude of light rays. When you have completed this activity, go to the one on Trichomacy to see how this works.